Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics

The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.Contents:

Introduction
Limiting Spectral Distributions
Extreme Eigenvalues
Central Limit Theorems of Linear Spectral Statistics
Limiting Behavior of Eigenmatrix of Sample Covariance Matrix
Wireless Communications
Limiting Performances of Linear and Iterative Receivers
Application to Finance



Readership: Graduate students and researchers in random matrices.